X.

1. ${\displaystyle \frac{10x+13}{18}}-{\displaystyle \frac{x+2}{x-3}}={\displaystyle \frac{5x-4}{9}}$.

2. ${\displaystyle \frac{6x+7}{10}}-{\displaystyle \frac{3x+1}{5}}={\displaystyle \frac{x-1}{3x-4}}$.

3. ${\displaystyle \frac{11x-12}{14}}-{\displaystyle \frac{11x-7}{19x+7}}={\displaystyle \frac{22x-36}{28}}$.

4. ${\displaystyle \frac{2x-1}{5}}+{\displaystyle \frac{2x-3}{17x-12}}={\displaystyle \frac{4x-3}{10}}$.

5. ${\displaystyle \frac{11x-13}{7}}-{\displaystyle \frac{13x+7}{3x+7}}={\displaystyle \frac{22x-75}{14}}$.

6. ${\displaystyle \frac{6x-13}{2x+3}}+{\displaystyle \frac{6x+7}{9}}-{\displaystyle \frac{2x+4}{3}}=0$.

141. Literal Equations.

Literal equations are equations in which some or all of the known numbers are represented by letters; the numbers regarded as known numbers are usually represented by the first letters of the alphabet.

1. Solve ${\displaystyle \frac{x+a}{x-b}}+{\displaystyle \frac{x+b}{x-a}}=2$.

Multiply by $(x-a)(x-b)$,

$(x+a)(x-a)+(x+b)(x-b)$ = 2(x - a)(x - b), lintor x^2 - a^2 + x^2 - b^2 = 2x^2 - 2ax - 2bx + 2ab. [1] lint Transpose, x^2 + x^2 - 2x^2 + 2ax + 2bx = a^2 + 2ab + b^2. [1] lint Combine, 2ax + 2bx = a^2 + 2ab + b^2, lintor 2(a + b)x = a^2 + 2ab + b^2. [1] lint Divide by $a+b$, 2x = a + b, x = a + b2.

Exercise 54.

Solve:

1. $a(x-a)=b(x-b)$.

2. $(a+b)x+(a-b)x=a^2$.

3. $(a+b)x-(a-b)x=b^2$.

4. $(2x-a)+(x-2a)=3a$.

5. $(x+a+b)+(x+a-b)=2b$.

6. $(x-a)(x-b)=x(x+c)$.

7. $x^2+b^2=(a-x)(a-x)$.

8. $(a+b)(2-x)=(a-b)(2+x)$.

9. $(x-a)(2x-a)=2(x-b{)}^2$.